There are many definitions of Mathematics. For many it is about arithmetic. For me, it is about getting correct answers with as little arithmetic as possible. Yes, it starts with counting and goes on from there.
We count in a number system created by the convenience of using our fingers on both hands. But, because ten is not dividable by three there are many examples where, for convenience, we do not use base ten. Most notable examples are: Time, and Angles where the basic unit: a full circle of the planet we live on is broken up into a number of pieces that is divisible by three. Other examples are: the dozen, feet & inches, and keys in a music octave.
It is unfortunate that God did not give us another thumb on each hand, mathematically six is a much better number than five, then we would have had twelve fingers, and counted base twelve instead of ten. He did wiseup and gave insects 6 legs! (A 5 legged criter would be stupid.)
Click here for more on this fantasy of changing the number system we use to be base twelve. I agree it would have many advantages, but when we can't in the USA get people to change to Metric; think how difficult it would be to change the base of the number system. We can't even change the stupid way many words are spelled in English. Tradition is a curse on human thinking.
Things I have written about:
Some of the pages are old, and some links may not
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